A Study on Twin Prime Numbers Distribution Based on Repetitive Pattern Analysis

The twin prime conjecture is a historically unsolved problem. Different from many previous approaches, this paper uses a 2-D mapping of odd numbers and subsequently transforms the 2-D mapping to reveal some base pattern regularity. Based on the repetitive base pattern analysis, a ratio, twin prime pairs per unit length, can be defined and calculated, thus a theoretical distribution can be derived which is very close to the trend of the average of the real distribution. Slight change in the calculation results in a lower average limit of twin prime pair distribution and consequently proves the twin prime conjecture